Monkey saddle

The graph of the monkey saddle function

The monkey saddle is a spatial surface that is described in a three-dimensional Cartesian coordinate system by the graph of the function . ${\ displaystyle f (x, y) = x ^ {3} -3xy ^ {2}}$

Characteristic of the function

The area is characterized by three elevations and three depressions that meet at the origin . The plane is axially symmetrical to the z-axis, namely with a rotation of 2 π / 3 rad or 120 ° with any orientation .

Origin of name

The name "monkey saddle" is derived from the similarity of the graph to the shape of a riding saddle . However, since there are three indentations for the two legs of the rider instead of two, the function “monkey saddle” was named; it found a further reduction in the tail of the monkeys .

Web links

Monkey saddle. In: Mathematik-Online-Lexikon. University of Stuttgart / University of Ulm , January 25, 2006, accessed on January 5, 2011 .
Model: Affensattel (two copies). In: Mathematical Models - Collection of the Technical University of Dresden . Retrieved January 5, 2011 .

Individual evidence

↑ Wolfgang Kühnel : Differential Geometry. Curves - surfaces - manifolds. 4th revised edition. Vieweg, Wiesbaden 2008, ISBN 978-3-8348-0411-2 , p. 51.

[1] Wolfgang Kühnel : Differential Geometry. Curves - surfaces - manifolds. 4th revised edition. Vieweg, Wiesbaden 2008, ISBN 978-3-8348-0411-2 , p. 51.